Calculation of bulk modulus and its pressure derivatives from vibrational frequencies and mode Gruneisen parameters: solids with cubic symmetry or one nearest-neighbor distance

The bulk modulus K_T can be related to structural parameters and to the sum of the squares of the vibrational frequencies, Σv_i², for N-atom crystals of cubic symmetry or for any symmetry that contains only one nearest-neighbor distance. Required assumptions are the existence of (1) electrostatic forces exclusively between atoms at equivalent positions in the primitive unit cell, (2) pair-wise central repulsive potentials between all other atoms, and (3) rigid ions. Including pressure in the derivation requires a more stringent version of point 2, namely, (4) that the structure scales isotropically upon compression. This leads to structurally independent formulas for the pressure derivatives of bulk modulus at 1 atm; the only variables are K_T and sums involving v_i² and the first or second pressurderivative of v_i, i.e., the mode Gruneisen parameters. Implicit in all equations is the independence of the sums on wave vector. Thus, knowledge of zone center phonons (mostly infrared and Raman bands) is sufficient to calculate elastic properties. -from Author